In the course of Awake, Detective Britten encounters certain situations and entities which he ultimately concludes are products of his imagination that he only perceived as real.
In the episode Say Hello to My Little Friend, Michael discovers Detective Ed Hawkins in the back seat of his car; he disappears when someone else approaches and reappears in the front seat. Since Michael seems confused, Hawkins explains that he must be a hallucination.
Kessel Murder - Although Michael did not witness the murder of Carl Kessel, he is able to perceive specific details of the event as if he'd been there. He is aided in this by Penguin-Suited Vega, see below.
Advice from Dr. Lee - When Michael works with Dr. Lee on a hostage situation, Lee appears to remain on the scene to counsel him about how to deal with the perpetrator. Later, Lee says that he actually left, leading Michael to conclude that he was hallucinating the Doctor.
The Penguin - On a few occasions, one during a therapy session with Dr. Evans, a penguin comes to give Michael inquisitive stares. It leads him to intuit that Rex is in possession of missing police evidence. It was apparently inspired by "That's Not My Penguin," a book he and his wife used to read to Rex.
Penguin-Suited Vega - Michael once perceives Vega in a penguin costume. Vega offers no explanation for the odd choice of outfits, only that it is less important than the fact that Michael can perceive the specifics of an event he could not logically have witnessed. (See Kessel Murder, above.)
Vega - See Penguin-Suited Vega, above.